A. In a given normal distribution, the sample mean is 75 and the sample standard deviation is 4. Find the corresponding standard score of the following values:
1. 69
2. 85
3. 70
4. 65
B. In a given normal distribution, the population standard deviation is 2.5. Find the corresponding standard score of the following values:
5. 78
6. 84
7. 76
8. 85
C. In a given normal distribution, the population mean is 60 and the population standard deviation is 3.2. Find the corresponding standard score of the following values:
9. 56
10. 74
11. 68
12. 52
In a given normal distribution, the sample mean is 75 and the sample standard deviation is 4. Find the corresponding standard score of the following values: a. 69 b. 85 c. 70 d. 65
Z = (score-mean)/SD
Insert values and solve for Z.
Need mean value for B.
I like tgat
To find the corresponding standard scores for the given values in a normal distribution, you need to use the formula:
Standard Score (z) = (x - mean) / standard deviation
Where:
- x represents the given value,
- mean represents the sample or population mean,
- and standard deviation represents the sample or population standard deviation.
Let's calculate the standard scores for each given value:
A. Given sample mean = 75 and sample standard deviation = 4.
1. For the value 69:
Standard Score (z) = (69 - 75) / 4
Standard Score (z) = -6 / 4
Standard Score (z) = -1.5
2. For the value 85:
Standard Score (z) = (85 - 75) / 4
Standard Score (z) = 10 / 4
Standard Score (z) = 2.5
3. For the value 70:
Standard Score (z) = (70 - 75) / 4
Standard Score (z) = -5 / 4
Standard Score (z) = -1.25
4. For the value 65:
Standard Score (z) = (65 - 75) / 4
Standard Score (z) = -10 / 4
Standard Score (z) = -2.5
B. Given population standard deviation = 2.5.
5. For the value 78:
Standard Score (z) = (78 - mean) / standard deviation
Standard Score (z) = (78 - mean) / 2.5
Since the mean is not provided, we can't calculate the exact standard score without knowing the mean.
6. For the value 84:
Standard Score (z) = (84 - mean) / 2.5
Similarly, without knowing the mean, we can't calculate the exact standard score.
7. For the value 76:
Standard Score (z) = (76 - mean) / 2.5
Again, without knowing the mean, we can't calculate the exact standard score.
8. For the value 85:
Standard Score (z) = (85 - mean) / 2.5
Without the mean, we can't calculate the exact standard score.
C. Given population mean = 60 and population standard deviation = 3.2.
9. For the value 56:
Standard Score (z) = (56 - 60) / 3.2
Standard Score (z) = -4 / 3.2
Standard Score (z) = -1.25
10. For the value 74:
Standard Score (z) = (74 - 60) / 3.2
Standard Score (z) = 14 / 3.2
Standard Score (z) = 4.375
11. For the value 68:
Standard Score (z) = (68 - 60) / 3.2
Standard Score (z) = 8 / 3.2
Standard Score (z) = 2.5
12. For the value 52:
Standard Score (z) = (52 - 60) / 3.2
Standard Score (z) = -8 / 3.2
Standard Score (z) = -2.5
To summarize:
A. Given sample mean = 75 and sample standard deviation = 4.
1. 69: Standard score (z) = -1.5
2. 85: Standard score (z) = 2.5
3. 70: Standard score (z) = -1.25
4. 65: Standard score (z) = -2.5
C. Given population mean = 60 and population standard deviation = 3.2.
9. 56: Standard score (z) = -1.25
10. 74: Standard score (z) = 4.375
11. 68: Standard score (z) = 2.5
12. 52: Standard score (z) = -2.5
Please note that for part B, without knowing the mean, we can't calculate the exact standard score.